1. Introduction

Finite-impulse-response microwave photonic filters (FIR-MPFs) are very attractive in high-performance radar, radio astronomy and millimeter-wave communications [1,2]. In a typical FIR-MPF, multiple taps are generated, controlled, and summed up after a time delay stage by all optical means, forming a discrete-time photonic microwave processor. Compared with its electrical counterparts, the FIR-MPF has the advantages of high frequency, tunability, reconfigurability and immunity to EMI.

However, there are still many difficulties to implement such a FIR-MPF with these full features. First is the all-positive system constraint, which implies that a baseband response always exists and is larger than the bandpass [3]. Another constraint is the dispersion induced carrier suppression effect (CSE) when traditional double-sideband intensity modulation is used [1]. This greatly limits the tunable range of the MPF. A third drawback with the discrete-time FIR-MPF is that the frequency response is periodic. Although plenty of methods have been proposed to solve each of these problems respectively [4–11], there are still few demonstrations which are free from these constrains simultaneously. Reference [12] presents a single-passband MPF with no baseband response by exploiting a dual-input Mach-Zehnder modulator and the RF decay effect due to the slice spectral width. Though tunability is shown in the paper, it is still challenging to tune the passband up to ultra-high frequencies (e.g. tens of GHz) because of the CSE. Reference [13] proposes a widely tunable chirped MPF based on nonlinear dispersion and a Mach-Zehnder interferometer before the photo detector. This also offers a way to implement non-chirped MPFs by using linear dispersive devices. The baseband response is eliminated through balanced detection, for which high balances of both power and time delay are required for the two optical paths.

Recently, widely tunable MPFs based on coherent multi-wavelength sources by using a tunable Mach-Zehnder configuration have been proposed and investigated intensely [14–16]. Frequency responses free from the baseband response and the CSE were demonstrated via this variable optical carrier time shift (VOCTS) method. But the utility frequency range of the MPFs is still limited by the free spectral range and the Nyquist zone.

In this paper, we demonstrate a novel MPF based on a non-coherent broadband optical source (BOS) and the VOCTS method. The BOS is low-cost and easy to get compared to optical frequency combs or mode-locked lasers. The much wider spectra also facilitate achievement of high Q factors. Traditionally, the BOS needs to be sliced to implement a MPF. Constrained by the short coherent time, the VOCTS method is not applicable to a sliced BOS as pointed out in [15]. We show here that by using a non-sliced BOS, equivalent “electrical slicing” is performed without the coherent problem. The resulting MPF fulfills the following three features: single bandpass, free from the CSE and the baseband response. Detailed theoretical and experimental investigations are presented which verifies our basic idea.

2. Theoretical principle

The experimental setup is shown in Fig. 1 . The BOS is polarized and split into two branches through an optical coupler. Branch 1 is intensity or phase modulated by the microwave input, while branch 2 is time shifted via a variable optical delay line (VDL). The two branches are then coupled together again with same polarizations and go through an optical dispersive device which is a length of dispersion-compensating fiber (DCF). The combined optical signals after dispersion are detected by a photo detector to generate the microwave output.

 

Fig. 1 Set up of the widely tunable single-bandpass microwave photonic filter. FBG: fiber Bragg grating; BOS: broadband optical source; PC: polarization controller; EOM: electro-optic modulator; VDL: variable delay line; DCF: dispersion-compensating fiber.

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The complex electrical field of the BOS is expressed as

and the stochastic property of $E(\Omega )$ is given by [17]

where $N(\Omega )$ is the power spectral density. Suppose that the light of branch 1 is modulated by a single-frequency microwave signal given by $\cos \left(j{\omega }_{e}t\right)$ where ${\omega }_e$ is the RF frequency, then under small-signal modulation and by considering only the first-order sidebands, the frequency-domain optical signal after modulation is written as

and the time shifted optical carrier of branch 2 is

Here, $c_1$, $c_2$ and m are strength factors; φ is the phase difference between the carrier and the sidebands depending on the modulation type, 0 for intensity modulation and $\pi /2$ for phase modulation; $\Delta \tau$ is the time shift between the two branches. The dispersive device is modeled as an optical phase filter given by ${\Phi }_d(\Omega )=\exp \left[-j{\beta }_2{\left(\Omega -{\Omega }_0\right)}^2/2\right]$, where ${\beta }_2$ is the total dispersion and ${\Omega }_0$ is the central frequency of the optical spectra. Then the signal currents generated by square-law detection of $O_1(\Omega )$ combined with $O_2(\Omega )$ after dispersion are

where $O_3(\Omega )=\left[O_1(\Omega )+O_2(\Omega )\right]{\Phi }_d(\Omega )$. For briefness, we omit the DC and the small second harmonic components here. The photo currents are composed of two parts: one part is generated by beating of the optical carriers with the sidebands both from branch1; the other is generated by beating of the optical carriers from branch2 with the sidebands from branch1. Recall that the frequency-domain input microwave signal is $\pi \left[\delta \left(\omega -{\omega }_e\right)+\delta \left(\omega +{\omega }_e\right)\right]$, the MPF’s transfer function is thus

where $H_b\left(\omega \right)$ is the baseband response defined by

The transfer function is composed of the baseband response and the bandpass response, corresponding to the two current parts mentioned above. The baseband response can be eliminated if carrier-suppression modulation ($c_1=0$) or phase modulation ($\phi =\pi /2$) is used. Then the MPF’s response will be a single passband which is widely tunable.

Different from conventional configurations based on BOSs, our configuration does not contain any explicit optical slicing stage. It is especially apparent when we use carrier-suppression modulation. Then the DC light of branch 1 is zero, so we cannot see periodic optical spectra after the second coupler. The physical fact is illustrated in Fig. 2 . Only the time-shifted optical carrier components from branch 2 and the sideband components from branch1 which contribute to the bandpass response are drawn. If we regard each carrier and two corresponding sidebands as is generated by modulation of one single source, then the modulation type changes between intensity modulation and phase modulation along the optical frequency axis. Thus a sinusoidal slicing function is generated electrically when the optical signals are intensity detected at the photo detector. The slicing period is given by $1/\Delta \tau$ which can be tuned by adjusting the VDL.

 

Fig. 2 Illustration of the variable optical carrier time shift method. Green arrows: sideband components from branch 1; Red arrows: time-shifted carrier components form branch 2; IM: intensity modulation; PM: phase modulation.

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The CSE with traditional MPF employing double-sideband intensity modulation is actually the dispersion induced modulation type evolution (DIME), which implies that the optical intensity modulation is translated to phase modulation and vice versa. The identical DIME is imposed on all the taps, thus on the transfer function. In our configuration, because of the periodically varying modulation type, the DIME only causes changes of the electrical slicing phase. The slicing amplitude is not affected, neither is the transfer function amplitude.

By comparing the results above with those of a MPF based on optical frequency combs (OFCs) [15], we can see that the BOS acts very much like a special optical frequency comb with infinite lines and infinitesimal spacing. The main differences between them are: for the OFC, the optical power concentrates at discrete frequency points and the phases of the optical components are correlated, so there are high interferences resulting from the optical carriers beating with each other and the modulation sidebands, this limits the MPF utility frequency range to the Nyquist zone [15]; but for the BOS, the optical power spreads continuously over a wide frequency range and the phases of the optical components are totally uncorrelated, then the interferences exhibit as a wideband noise which can be further reduced significantly via balanced detection [18]. Furthermore, the infinitesimal frequency spacing of the BOS gives rise to a continuous impulse response and an infinite free-spectral range, thus single passband is achievable.

3. Experimental results and discussion

We used the spontaneous emission from an Erbium-doped fiber amplifier as the BOS. The optical spectra were adjusted by a fiber Bragg grating with a bandwidth of 5 nm, as shown in the inset of Fig. 1. The 8-km DCF has a total dispersion of $8.55\times {10}^{-22}{\text{ s}}^2$ (671.2 ps/nm).

We compared the responses of the traditional spectrum-sliced MPFs [9,10] with those of our configuration. A Mache-Zehnder intensity modulator was used first and the experimental and theoretical results are shown in Fig. 3 . The 3-dB bandwidth of the MPF is ~228 MHz with the effect of the slight dispersion slope [9]. The bandpass center was tuned from 2 GHz to 18 GHz with a 2-GHz step, by changing the time delay in the lower arm of the Mache-Zehnder structure from 10.7 ps to 96.7 ps with a step of ~10.7 ps. For the traditional configuration proposed in [9], the bandpass amplitude is seriously suppressed at 10 GHz and 16 GHz due to DIME, as shown in Figs. 3 (a.1) and (a.2). But for our configuration, the bandpass amplitude keeps nearly constant when the frequency is tuned, as shown in Figs. 3 (b.1), (b.2), (c.1), and (c.2). The responses of the modulator, photo detector and microwave amplifier have been subtracted. The remaining fluctuation of the passband peak is about 1.5 dB. For Figs. 3 (b.1) and (b.2), the modulator was biased at the quadrature point and the DC optical power of branch 1 and branch 2 were equal. There is always a baseband response which is about 6 dB higher than the bandpass. As we have analyzed above, the baseband response is eliminate when the modulator is biased at the carrier-suppression point, as proved in Figs. 3 (c.1) and (c.2).

 

Fig. 3 Tunable filter response when Mache-Zehnder intensity modulator is used. (a.1), (a.2) Traditional configuration; (b.1), (b.2), (c.1), (c.2) our configuration with the modulator biased at quadrature point and carrier-suppression point, respectively. (a.1), (b.1), (c.1) Experiment, (a.2), (b.2), (c.2) theory.

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We then changed the intensity modulator for a phase modulator, and the results are shown in Fig. 4 . There is always no baseband response when phase modulation is used. But the tunability is still constrained by the DIME for the traditional configuration [10], as shown in Figs. 4 (a.1) and (a.2). For our configuration, the DIME is avoided while the baseband response keeps absent, as shown in Figs. 4 (b.1) and (b.2). The advantage of using optical phase modulation is that the modulator has no bias drift problem and does not need any bias control, thus the system is more simple and stable.

 

Fig. 4 Tunable filter response when phase modulator is used. (a.1), (a.2) Traditional configuration; (b.1), (b.2) our configuration. (a.1), (b.1) Experiment, (a.2), (b.2) theory.

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We found in experiments that though a Mache-Zehnder structure was used, the amplitude responses of the MPF were not sensitive to the environmental disturbances, as also proved in [9,10]. We also calculated the theoretical results in all cases with the measured optical spectra, and excellent agreements between the experimental and theoretical results are obtained.

4. Conclusions

We have proposed a very promising way to implement widely tunable real single-bandpass MPF with the advantages of low cost and simple structure. The basic idea is to form an electrical slicing function by combining the time-shifted broadband optical carrier with the sidebands generated by modulation. Due to the periodic changes of the modulation type between intensity modulation and phase modulation along the optical frequency axis, the DIME can be avoided. Furthermore, by using optical carrier-suppression modulation or phase modulation, the baseband response can also be eliminated. Detailed theoretical and experimental investigations are presented which agree with each other quite well.